This paper proposes the notion of exhaustion as an alternative paradigm to study postwar historiographies of computer-aided architecture. Delving into a new case study—the Calculation Center of the University of Madrid—it aims to respond to the following question: why was the computer consistently described as a tool that would expedite design work and yet used to produce delirious and repetitive combinatorial architectural designs? This paper characterizes such designs as exhaustive. Exhaustion—unlike efficiency or optimization—was time-consuming and costly yet considered worthy because it promised variability within a repetitive step-by-step process. In the pursuit of exhaustion, architects developed a new vocabulary of “variations,” “alternatives,” and “choices” that promised to express change within a step-by-step recurring methodology.